Assessment of depression in veterans across missions: a validity study using Rasch measurement models

Figures & data

Table 1. Items in the 10-item PRIM-Depression scale.*

How often did you experience the following during the last three months?
1. Were you easily saddened?
2. Did you have thoughts about taking your own life?
3. Did you have worries about the future?
4. Did you feel sad?
5. Did you feel inferior or insecure?
6. Did you feel empty inside?
7. Did you feel abandoned?
8. Did you worry a lot?
9. Did you feel like something inside was broken?
10. Did you feel that everything was meaningless?

*Items appear in Danish in the original questionnaire and have been translated for the purpose of this study.

Table 2. Global test of fit and differential item function for the 10-item and the 8-item PRIM-Depression scale.

Item difficulties for the graphical log-linear Rasch model for the 10-item PRIM-Depression scale.

	10-item PRIM-Depression, RM			10-item PRIM-Depression, GLLRM**			8-item PRIM-Depression, RM
Tests of fit	CLR	df	p	CLR	df	p	CLR	df	p
Global homogeneity	18.1	9	.03*	18.7	11	.07	14.3	7	.05
Global DIF relative to
Danger	8.0	9	.53	7.0	11	.80	4.4	7	.73
Contract	7.2	9	.61	15.7	11	.15	6.5	7	.49
Previous deployment	11.5	9	.25	13.2	11	.28	11.4	7	.12
Gender	9.1	9	.43	10.5	11	.49	6.4	7	.49
Age group	16.9	9	.05	22.9	11	.02*	10.7	7	.15
Cohort	29.6	9	< .001	5.7	7	.57	6.0	7	.54

CLR = Conditional likelihood ratio test. df = Degrees of freedom. DIF = Differential item function. GLLRM = Graphical log-linear Rasch model. RM = Rasch model.

All p-values were adjusted for false discovery rate (FDR) by using the Benjamini-Hochberg procedure.

*p-values that were above the 5% critical limit after the adjustment for FDR

(** The GLLRM for the 10-item PRIM-Depression scale included DIF for item 3 and item 8 relative to cohort; see also Table 3).

Table 3. Item difficulties for the graphical log-linear Rasch model for the 10-item PRIM-Depression scale.

Item	Item difficulties in logits, 10-item PRIM-Depression scale	Item difficulties in logits, 8-item PRIM-Depression scale
1	−0.54	−1.15
2	3.76	3.16
3 Cohort 2
2	−2.06
3 Cohort 1
1	−0.94
4	−2.38	−3.08
5	−0.04	−0.63
6	−0.23	−0.82
7	1.43	0.84
8 Cohort 2
2	−2.79
8 Cohort 1
1	−1.84
9	1.30	0.72
10	1.55	0.97

Table 4. Effect of differential item function on the total score of the 10-item PRIM-Depression scale.

	Observed and DIF-equated total sum scores (#)
	# Obs Cohort 2	# Obs Cohort 1	# Equated Cohort 1
Mean	3.07	3.51	3.74*
SD	2.82	2.86	2.82
SE	0.17	0.16	0.15

DIF = Differential item function. # Obs = observed total score. # Equated = equated total score.

The effect of the cohort-DIF can be seen as the difference between the observed and equated mean scores for Cohort 1 compared to Cohort 2.

* = Hypothesis of equality is rejected for equated mean score Cohort 1 and observed mean score Cohort 2 (p < .001).

Table 5. Score equation for Cohort 1 to adjust for cohort-differential item function in the 10-item PRIM-Depression scale.

Cohort 2 sum scores	Cohort 1 DIF-equated scores
1.00	1.39
2.00	2.49
3.00	3.44
4.00	4.33
5.00	5.23
6.00	6.14
7.00	7.08
8.00	8.04
9.00	9.01

DIF = Differential item function.

Maximum and minimum scores are not shown, as no equation is possible of extreme scores.

Table 6. Targeting and reliability of the 10-item and the 8-item PRIM-Depression scale.

	Theta				Sum score
Groups defined by danger, age group, cohort	Target	Mean	Test inf. Target index	RMSE target index	Target	Mean	Mean SEM	Reliability
	10-item PRIM-Depression scale
Low, < 30 years, Cohort 2	0.12	−1.94	0.626	0.759	5.23	3.07	0.90	0.89
High, < 30 years, Cohort 2	0.12	−0.41	0.803	0.911	5.23	4.54	1.07	0.84
Low, ≥ 30 years, Cohort 2	0.12	−2.54	0.584	0.724	5.23	2.53	0.86	0.88
High, ≥ 30 years, Cohort 2	0.12	−1.16	0.732	0.870	5.23	3.78	1.00	0.86
Low, < 30 years, Cohort 1	−0.10	−1.58	0.663	0.796	4.63	2.96	0.99	0.84
High, < 30 years, Cohort 1	−0.10	−0.52	0.739	0.810	4.63	4.14	1.07	0.85
Low, ≥ 30 years, Cohort 1	−0.10	−2.61	0.479	0.598	4.63	2.48	0.78	0.91
High, ≥ 30 years, Cohort 1	−0.10	−1.38	0.635	0.769	4.63	3.34	0.96	0.88
Groups defined by danger and gender (N)	8-item PRIM-Depression scale
Low, male (300)	0.00	−2.89	0.477	0.650	4.01	1.73	0.72	0.86
High, male (205)	0.00	−1.45	0.648	0.827	4.01	2.69	0.89	0.83
Low, female (28)	0.00	−1.58	0.598	0.773	4.01	2.64	0.85	0.87

RMSE = The root mean squared error. SEM = The standard error of measurement of the observed score.

Targeting and reliability has been estimated for all groups defined by exogenous variables involved in differential item function (Cohort in the case of the 10-item PRIM-Depression scale) as well as exogenous variables associated with the score (Danger and Age group in the case of the 10-item PRIM-Depression scale, and Danger and Gender in the case of the 8-item PRIM-depression scale).